Tidal stream turbine (TST) has the potential to become a key enabling technology for sustainable electricity supply in remote islands and coastal communities. This type of turbines are typically employed under water and subject to various external disturbances. These external disturbances make the development of control system for TST very challenging. A comprehensive continuous sliding-mode (CSM) control approach has been developed in this work for high-performance control of TST. First, a continuous twisting algorithm (CTA) is applied for robust regulation of the rotational speed under various marine current disturbances. Then, a multi-variable generalized super twisting controller is applied for current regulation that takes into account the cross-coupling effect in the current dynamics. Through numerical simulation, the performance of the proposed comprehensive CSM control technique is tested over the active disturbance rejection controller (ADRC).